Pressure oscillations with ultra-low frequency induced by vortical flow inside Francis turbine draft tubes

Abstract

The present paper aims to reveal the flow mechanism for the pressure oscillations with ultra-low frequency captured by the model test of Francis turbine operated at part-load condition. The experimental results indicate that the precessing vortex rope (PVR) induces the dominant pressure oscillation in the draft tube, and its frequency i.e. fPVR is one-fifth of runner rotation frequency (15.12 Hz). To investigate the PVR evolution in the turbine, numerical simulations based on the MSST PANS (modified SST based partially-averaged Navier-Stokes) model have been conducted, and the DMD (dynamic mode decomposition) method has been applied to analyze the modes for unstable flow inside the draft tube. To make out the effect of draft tube structure on the PVR and pressure oscillation, the conventional elbow-type draft tube i.e. EDT, and the conical draft tube i.e. CDT are treated for comparison. Under non-cavitation operation, both experiment and simulation capture two pressure oscillation components with ultra-low frequencies near fPVR/3 and 2fPVR/3. The analysis based on internal flow and DMD method depicts that the pressure oscillations with ultra-low frequency occur due to the strong interaction between the PVR and the backflow in the draft tube, and the elbow structure promotes the interaction and the swirling flow in the draft tube. It is also noted that the cavitation remarkably changes the dynamic characteristics of the precessing vortex rope in the draft tube. Further, cavitation alleviates the interaction between the PVR and backflow at the rear part of the PVR and suppresses the pressure oscillations with ultra-low frequency in the draft tube. Finally, it is confirmed that DMD analysis is helpful to depict the modal of the flow field and make out the important flow structure at various operations in the draft tube.